Four Odd Numbers
Years 2 - 8

This investigation has several levels of challenge. You don't have to do it all. Like a video game, you can stop at any level then return later for the next level. Keep good journal notes so you know the level you reached.

Preparation

  • Gather a collection of about 30 small objects, for example, buttons, plastic screw caps, pebbles, pasta - it doesn't matter what as long as you don't mess up the house.
  • Print a piece of Square Line Paper.
  • Write the title of this challenge and today's date on a fresh page in your maths journal.
When the activity is over your recording sheet should be put into your journal beside any other notes you make.

Making Numbers

  • Take a handful of objects from your collection. Pretend they are children. Arrange them so they are lined up to walk into class.
  • Did you arrange them in twos (2s)?
    That's how it usually happens in school.
    Check that yours are arranged in pairs.
  • Use your square line paper to make a drawing of your children like this ... and write the number of children.


    Near this picture you would write ten (10) children.
  • Put your children back in the collection.
    Choose a bigger or smaller handful.
    Arrange the children in twos.
    Do another drawing and write the number of children.
  • Keep doing this until you have five (5) drawings.
Your drawings look like this ... ... or like this ...
Whole numbers that line up in twos with one sticking out on the end are called ... ODD numbers.

Whole numbers that line up in twos exactly are called ... EVEN numbers.

  • In your journal write a list of the odd numbers you have found so far.
  • Write another list of even numbers you have found so far.
  • You can put the two lists side by side in a table if you know how to do that.
Without using your objects put more numbers in each list so that both lists have ten (10) numbers.
  • Are you sure you put them in the correct list?
  • How do you know?
  • Can you check it another way?

Have fun exploring Four Odd Numbers.

Puzzle: Four Odd Numbers

  • Open this Professor Morris Puzzle. (Artist: Rob Mullarvey)
    You can read it on screen ... or print it if you wish.
  • When you have found the four numbers, draw them on your paper.
  • Cut them out and write the number on each picture.
  • Move your number drawings around and try to fit them together.
  • Write and draw, or stick your drawings in your journal to explain what you find out.

Digging Deeper

Ria explored even numbers.

She noticed something about odd numbers, even numbers and times tables.

  • Cut out the next three even numbers and stick them in your journal like Ria.
  • Explain what she might have noticed.
So odd numbers and even numbers are connected.
Explain in words what these mean:
  • O + O = E
  • E + E = E
What do you think is the answer to O + E = ...?
What do you think is the answer to O + O + O + O = ...?
What do you think is the answer to E + E + E + E = ...?

Working Backwards

Write a list of all the odd numbers in order up to 20.
  • From the list, choose any four (4) odd numbers not the same. What is the smallest total you can make?
  • From the list, choose any four (4) odd numbers not the same. What is the largest total you can make?
  • From the list, choose any four (4) odd numbers not the same that add up to 40.
  • Can you do it a different way?
  • How many different ways can you do it?
  • How do you know when you have found them all?
  • What is the next number that can be a total of four different odd numbers?
        Can you explain why?

Generalising

  1. If I tell you any even number, can you tell me if it can be a total of four (4) odd numbers?
  2. If I tell you any even number that can be a total of four (4) odd numbers, can you tell me how to find them?

Just Before You Finish

For this part you need your maths journal and your Working Like A Mathematician page.
  • How did you work like a mathematician today? Record 2 ways.
  • What do you know now that you didn't know when you started Four Odd Numbers?

 

Send any comments or photos about this activity and we can start a gallery here.

 

Maths At Home is a division of Mathematics Centre